LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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cungql.f
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1*> \brief \b CUNGQL
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cungql.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cungql.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cungql.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, K, LDA, LWORK, M, N
25* ..
26* .. Array Arguments ..
27* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
28* ..
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> CUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
37*> which is defined as the last N columns of a product of K elementary
38*> reflectors of order M
39*>
40*> Q = H(k) . . . H(2) H(1)
41*>
42*> as returned by CGEQLF.
43*> \endverbatim
44*
45* Arguments:
46* ==========
47*
48*> \param[in] M
49*> \verbatim
50*> M is INTEGER
51*> The number of rows of the matrix Q. M >= 0.
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*> N is INTEGER
57*> The number of columns of the matrix Q. M >= N >= 0.
58*> \endverbatim
59*>
60*> \param[in] K
61*> \verbatim
62*> K is INTEGER
63*> The number of elementary reflectors whose product defines the
64*> matrix Q. N >= K >= 0.
65*> \endverbatim
66*>
67*> \param[in,out] A
68*> \verbatim
69*> A is COMPLEX array, dimension (LDA,N)
70*> On entry, the (n-k+i)-th column must contain the vector which
71*> defines the elementary reflector H(i), for i = 1,2,...,k, as
72*> returned by CGEQLF in the last k columns of its array
73*> argument A.
74*> On exit, the M-by-N matrix Q.
75*> \endverbatim
76*>
77*> \param[in] LDA
78*> \verbatim
79*> LDA is INTEGER
80*> The first dimension of the array A. LDA >= max(1,M).
81*> \endverbatim
82*>
83*> \param[in] TAU
84*> \verbatim
85*> TAU is COMPLEX array, dimension (K)
86*> TAU(i) must contain the scalar factor of the elementary
87*> reflector H(i), as returned by CGEQLF.
88*> \endverbatim
89*>
90*> \param[out] WORK
91*> \verbatim
92*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
93*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
94*> \endverbatim
95*>
96*> \param[in] LWORK
97*> \verbatim
98*> LWORK is INTEGER
99*> The dimension of the array WORK. LWORK >= max(1,N).
100*> For optimum performance LWORK >= N*NB, where NB is the
101*> optimal blocksize.
102*>
103*> If LWORK = -1, then a workspace query is assumed; the routine
104*> only calculates the optimal size of the WORK array, returns
105*> this value as the first entry of the WORK array, and no error
106*> message related to LWORK is issued by XERBLA.
107*> \endverbatim
108*>
109*> \param[out] INFO
110*> \verbatim
111*> INFO is INTEGER
112*> = 0: successful exit
113*> < 0: if INFO = -i, the i-th argument has an illegal value
114*> \endverbatim
115*
116* Authors:
117* ========
118*
119*> \author Univ. of Tennessee
120*> \author Univ. of California Berkeley
121*> \author Univ. of Colorado Denver
122*> \author NAG Ltd.
123*
124*> \ingroup ungql
125*
126* =====================================================================
127 SUBROUTINE cungql( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
128*
129* -- LAPACK computational routine --
130* -- LAPACK is a software package provided by Univ. of Tennessee, --
131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*
133* .. Scalar Arguments ..
134 INTEGER INFO, K, LDA, LWORK, M, N
135* ..
136* .. Array Arguments ..
137 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 COMPLEX ZERO
144 parameter( zero = ( 0.0e+0, 0.0e+0 ) )
145* ..
146* .. Local Scalars ..
147 LOGICAL LQUERY
148 INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
149 \$ NB, NBMIN, NX
150* ..
151* .. External Subroutines ..
152 EXTERNAL clarfb, clarft, cung2l, xerbla
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC max, min
156* ..
157* .. External Functions ..
158 INTEGER ILAENV
159 REAL SROUNDUP_LWORK
160 EXTERNAL ilaenv, sroundup_lwork
161* ..
162* .. Executable Statements ..
163*
164* Test the input arguments
165*
166 info = 0
167 lquery = ( lwork.EQ.-1 )
168 IF( m.LT.0 ) THEN
169 info = -1
170 ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
171 info = -2
172 ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
173 info = -3
174 ELSE IF( lda.LT.max( 1, m ) ) THEN
175 info = -5
176 END IF
177*
178 IF( info.EQ.0 ) THEN
179 IF( n.EQ.0 ) THEN
180 lwkopt = 1
181 ELSE
182 nb = ilaenv( 1, 'CUNGQL', ' ', m, n, k, -1 )
183 lwkopt = n*nb
184 END IF
185 work( 1 ) = sroundup_lwork(lwkopt)
186*
187 IF( lwork.LT.max( 1, n ) .AND. .NOT.lquery ) THEN
188 info = -8
189 END IF
190 END IF
191*
192 IF( info.NE.0 ) THEN
193 CALL xerbla( 'CUNGQL', -info )
194 RETURN
195 ELSE IF( lquery ) THEN
196 RETURN
197 END IF
198*
199* Quick return if possible
200*
201 IF( n.LE.0 ) THEN
202 RETURN
203 END IF
204*
205 nbmin = 2
206 nx = 0
207 iws = n
208 IF( nb.GT.1 .AND. nb.LT.k ) THEN
209*
210* Determine when to cross over from blocked to unblocked code.
211*
212 nx = max( 0, ilaenv( 3, 'CUNGQL', ' ', m, n, k, -1 ) )
213 IF( nx.LT.k ) THEN
214*
215* Determine if workspace is large enough for blocked code.
216*
217 ldwork = n
218 iws = ldwork*nb
219 IF( lwork.LT.iws ) THEN
220*
221* Not enough workspace to use optimal NB: reduce NB and
222* determine the minimum value of NB.
223*
224 nb = lwork / ldwork
225 nbmin = max( 2, ilaenv( 2, 'CUNGQL', ' ', m, n, k, -1 ) )
226 END IF
227 END IF
228 END IF
229*
230 IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k ) THEN
231*
232* Use blocked code after the first block.
233* The last kk columns are handled by the block method.
234*
235 kk = min( k, ( ( k-nx+nb-1 ) / nb )*nb )
236*
237* Set A(m-kk+1:m,1:n-kk) to zero.
238*
239 DO 20 j = 1, n - kk
240 DO 10 i = m - kk + 1, m
241 a( i, j ) = zero
242 10 CONTINUE
243 20 CONTINUE
244 ELSE
245 kk = 0
246 END IF
247*
248* Use unblocked code for the first or only block.
249*
250 CALL cung2l( m-kk, n-kk, k-kk, a, lda, tau, work, iinfo )
251*
252 IF( kk.GT.0 ) THEN
253*
254* Use blocked code
255*
256 DO 50 i = k - kk + 1, k, nb
257 ib = min( nb, k-i+1 )
258 IF( n-k+i.GT.1 ) THEN
259*
260* Form the triangular factor of the block reflector
261* H = H(i+ib-1) . . . H(i+1) H(i)
262*
263 CALL clarft( 'Backward', 'Columnwise', m-k+i+ib-1, ib,
264 \$ a( 1, n-k+i ), lda, tau( i ), work, ldwork )
265*
266* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
267*
268 CALL clarfb( 'Left', 'No transpose', 'Backward',
269 \$ 'Columnwise', m-k+i+ib-1, n-k+i-1, ib,
270 \$ a( 1, n-k+i ), lda, work, ldwork, a, lda,
271 \$ work( ib+1 ), ldwork )
272 END IF
273*
274* Apply H to rows 1:m-k+i+ib-1 of current block
275*
276 CALL cung2l( m-k+i+ib-1, ib, ib, a( 1, n-k+i ), lda,
277 \$ tau( i ), work, iinfo )
278*
279* Set rows m-k+i+ib:m of current block to zero
280*
281 DO 40 j = n - k + i, n - k + i + ib - 1
282 DO 30 l = m - k + i + ib, m
283 a( l, j ) = zero
284 30 CONTINUE
285 40 CONTINUE
286 50 CONTINUE
287 END IF
288*
289 work( 1 ) = iws
290 RETURN
291*
292* End of CUNGQL
293*
294 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine clarfb(side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition clarfb.f:197
subroutine clarft(direct, storev, n, k, v, ldv, tau, t, ldt)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition clarft.f:163
subroutine cung2l(m, n, k, a, lda, tau, work, info)
CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (un...
Definition cung2l.f:114
subroutine cungql(m, n, k, a, lda, tau, work, lwork, info)
CUNGQL
Definition cungql.f:128